**Description of a Solid Metal Sphere and Iron Rod System**A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. An iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicularly to the ends of the rod, as shown in the diagram, each with a force of 6.80 Newtons, causing the whole assembly to spin.**Tasks:**(a) Find the total moment of inertia, \( I \), of the sphere-rod combination.(b) Find the angular acceleration of the system.**Diagram Explanation:**The image displays a solid metal sphere with an iron rod inserted through its diameter. At each end of the rod, arrows indicate the direction of the force exerted by the rockets, perpendicular to the rod, which contributes to the spinning motion. The resultant forces are shown acting on opposite ends of the rod. **FORMULAS**- \( s = r\theta \), \( v = r\omega \), \( a = r\alpha \)- Torque: \( \tau = F(\sin\theta)r \)- \( \tau = Fl \), where \( l \) = lever arm**Equilibrium:** - \( \Sigma \tau = 0 \) **Non-equilibrium:** - \( \Sigma \tau = I\alpha \)---**Moments of Inertia for Various Rigid Objects of Uniform Composition: Point Mass: \( I = MR^2 \)****Diagrams Explanation:**1. **Hoop or Thin Cylindrical Shell:** - Diagram shows a circular object with thin walls. - Moment of Inertia: \( I = MR^2 \).2. **Solid Sphere:** - Diagram illustrates a filled sphere. - Moment of Inertia: \( I = \frac{2}{5} MR^2 \).3. **Solid Cylinder or Disk:** - Diagram represents a solid circular cylinder. - Moment of Inertia: \( I = \frac{1}{2} MR^2 \).4. **Thin Spherical Shell:** - Diagram shows a hollow sphere. - Moment of Inertia: \( I = \frac{2}{3} MR^2 \).5. **Long, Thin Rod with Rotation Axis Through Center:** - Diagram depicts a horizontal rod rotating around its center. - Moment of Inertia: \( I = \frac{1}{12} ML^2 \).6. **Long, Thin Rod with Rotation Axis Through End:** - Diagram shows a horizontal rod rotating around one end. - Moment of Inertia: \( I = \frac{1}{3} ML^2 \).---- \( s = r\theta \), \( v = r\omega \), \( a = r\alpha \)- Torque: \( \tau = F(\sin\theta)r \)- \( \tau = Fl \), where \( l \) = lever arm**Equilibrium:** - \( \Sigma \tau = 0 \)**Non-equilibrium:** - \( \Sigma \tau = I\alpha \)

Answered: Image /qna-images/answer/774cb2c7-41dd-488c-9e66-813970082c98.jpg

A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends of the rods as shown, each with a force of 6.80 Newtons, causing the whole thing to spin. (a) Find the total moment of inertia, I, of the sphere-rod combination. (b) Find the angular acceleration of the system.

A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends of the rods as shown, each with a force of 6.80 Newtons, causing the whole thing to spin. (a) Find the total moment of inertia, I, of the sphere-rod combination. (b) Find the angular acceleration of the system.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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